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Some comtinuous systems are directly related to particle systems through ultradiscretization. For example, we obtain the elementary cellular automaton of rule 184, the box and ball system and the ultradiscrete Toda equation by ultradiscretizing the Burgers equation, the KdV equation and the Toda equation respectively.
In my talk, I will report some particle systems of cellular automaton type. The space and time variables are both discrete and the dependent variable is binary in the systems. Their common features are the conservation of the number of particles and the direct relation to the continuous systems, for example, a system of ordinary differential equations or a partial differential equation.
Moreover, behavior of solutions, mathematical features and physical aspect of each system will also be discussed. 
